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Wishing to explore the complexity of the conceptual, didactic and institutional aspects of learning a scientifically defined object of knowledge, we chose to study the link between the personal relation to numeration developed by six-year-old pupils in first grade (“cours préparatoire” the first level of primary school in France), and more particularly, the relationship between the construction of pupils’ relation to the concept of “tens” and the didactic practice of their teachers during the lessons.
Our study shows that both teachers establish “strong” didactic contracts, leaving it up to the pupils to develop on their own the capacity of making mathematical decisions and destabilizing the procedure of counting one by one. There is a difference between classes in the articulation of knowledge and know-how. In the ZEP class learning is centered on know-how; in the other class knowledge and know-how are simply juxtaposed, their relationship is never made explicit. The result is that only 4 children out of 42 (the two classes taken together) can work with both. All four belong to the categories of “good” or “very good” students.
